EP3018625B1 - Method for calibrating a sight system - Google Patents

Description

FIELD OF THE INVENTION

The invention relates to a method of calibrating a sighting system for aiming an object by means of a viewfinder, the position of the object being located in a repository external to the viewfinder, and a system implementing said method.

The invention finds application in particular in the field of acquiring high-resolution images at a precise position, such as the acquisition of biometric feature images of individuals.

STATE OF THE ART

Calibration of a sighting system is the determination of a control law to be applied to a viewfinder to enable, from a position of an object in a repository external to the viewfinder, to orient said viewfinder so as to aim at the object.

An example of an application is a system for acquiring images of biometric traits of individuals, such as, for example, iris images. In order to acquire high resolution images of an individual's iris, the system requires a high-resolution camera. Because of this important resolution, this camera can not have a wide fixed field, but must be mobile in order to be able to aim at an iris of an individual.

The system thus also includes two cameras of lower resolution, but wide field, and fixed, which can detect the position of an iris of an individual.

The position of the iris in the repository of the large-field cameras must be exploited by the high-resolution camera to aim at the iris and then proceed to its acquisition.

In this type of system, the determination of the control law of the aiming camera (in the preceding example: the high-resolution camera) was made from a prior kinematic model of the system comprising the whole cameras.

This model makes it possible to estimate the relative positions of the various cameras of the system, and according to these positions, the position of the object in the repository of the aiming camera, then the commands to be applied to this camera to aim at the object. .

However, this approach has many problems. First of all, the determination of a kinematic model must be implemented for each new aiming system, since the model depends on the relative positions between the different components of the system. But this process of determining the kinematic model is long and complex.

In addition, this approach may require, in order to simplify the kinematic model, to simplify the design of the sighting system, which can be binding.

Finally, this approach is very restrictive in terms of mechanical precision during the manufacture of the sighting system to ensure the relevance of the kinematic model once the sighting system assembled.

Precision errors may occur if the aiming system has not been assembled with the required accuracy and if there are discrepancies between the prior model and the actual system.

Another solution has been proposed in the article of Junejo, IN, and Foroosh, H, Optimizing PTZ camera calibration from two images, Machine Vision and Applications, 23 (2), 375-389; 2012 .

Nevertheless this method requires to acquire two images with a recovery of views, so for a large focal length, with a small angular difference between the shots, which is constraining and unfavorable to accuracy.

The document US 2010/0289869 describes another type of calibration of a camera, including the determination of intrinsic and extrinsic parameters of a camera, the extrinsic parameters including in particular the angles of view of the camera with respect to a point, from the commands of the camera for aim for the point.

This document does not make it possible to establish a control law to be applied to the camera to reach these viewing angles. In addition, this document can not be applied in the case of acquisition of iris images because the long focal length used for this purpose prevents precise determination of the intrinsic and extrinsic parameters of the camera.

PRESENTATION OF THE INVENTION

The object of the invention is to propose a method for calibrating a sighting system that is simple and quick to implement, and less restrictive on the design and manufacture of the sighting system.

The invention also aims to propose a universal calibration method, that is to say not dependent on the composition or the structure of the sighting system.

• viser, avec le viseur des objets se trouvant à au moins six positions différentes connues dans le référentiel du système de visée et relever les commandes correspondantes,
• à partir des positions de l'objet et des commandes correspondantes, déterminer la position du point concourant des lignes de visées et la loi de commande par la minimisation d'une fonction de la dérivée seconde de la loi de commande.

In this regard, the subject of the invention is a method of calibrating a sighting system comprising a viewfinder and an optical device for detecting the position of an object in space, characterized in that it comprises the determination of a control law to be applied to the viewfinder to aim the object according to its position, said position being determined in a repository of the detection optics and the control law comprising two angular commands and a control of development of the viewfinder, expressed as a function of the relative positions between the object to be aimed at and a common point of all the lines of sight of the viewfinder,
the method comprising the steps of:

• aim, with the viewfinder, objects found in at least six different positions known in the reference system of the aiming system and record the corresponding commands,
• from the positions of the object and the corresponding commands, determining the position of the point constituting the lines of sight and the control law by minimizing a function of the second derivative of the control law.

• l'étape de détermination de la position du point concourant et de la loi de commande comprend la mise en oeuvre des étapes consistant à :
  • ∘ déterminer une position du point concourant correspondant à des commandes minimisant la fonction de la dérivée seconde de la loi de commande, et
  • ∘ une fois la position du point concourant déterminée, déterminer les commandes minimisant la fonction de la dérivée seconde de la loi de commande.
• l'étape de détermination de la position du point concourant comprend la minimisation, en fonction de ladite position, de l'intégrale de la somme des dérivées secondes des commandes angulaires.
• l'étape de détermination de la position du point concourant comprend la minimisation, en fonction de ladite position, de l'intégrale de la somme des dérivées secondes des positions angulaires relatives entre le point à viser et le point concourant exprimées en fonction des commandes angulaires du viseur.
• chaque commande angulaire est une fonction de deux angles de type spline de plaque mince.
• chaque commande angulaire est une fonction de deux angles du type spline de plaque mince régularisée.
• la détermination de la commande de mise au point est mise en oeuvre lors de la détermination des commandes angulaires ou postérieurement à la détermination des commandes angulaires et du point M.
• la détermination de la commande de mise au point comprend la minimisation de l'intégrale de la dérivée seconde de la commande de mise au point.
• la commande de mise au point est une fonction de type spline cubique.

Advantageously, but optionally, the method according to the invention may further comprise at least one of the following characteristics:

• the step of determining the position of the concurrent point and the control law comprises the implementation of the steps of:
  • Determining a position of the concurrent point corresponding to commands minimizing the function of the second derivative of the control law, and
  • ∘ Once the position of the concurrent point determined, determine the commands minimizing the function of the second derivative of the control law.
• the step of determining the position of the concurrent point comprises the minimization, as a function of said position, of the integral of the sum of the second derivatives of the angular commands.
• the step of determining the position of the concurrent point comprises the minimization, as a function of said position, of the integral of the sum of the second derivatives of the relative angular positions between the point to be aimed and the concurrent point expressed as a function of the angular commands of the viewfinder.
• each angular control is a function of two spline angles of thin plate.
• each angular control is a function of two angles of the regularized thin plate spline type.
• the determination of the focus control is carried out during the determination of the angular commands or after the determination of the angular commands and the point M.
• determining the focus control includes minimizing the integral of the second derivative of the focus control.
• focus control is a cubic spline function.

The invention also relates to an aiming system comprising a viewfinder, an optical system for detecting a position of an object to be aimed at, and a processing unit comprising processing means, the aiming system being characterized in that is adapted to implement the method according to the foregoing description.

• acquérir une position d'un objet à viser dans un référentiel de l'optique de détection,
• déduire des positions relatives entre l'objet et un point concourant des lignes de visée du viseur, des coordonnées de l'objet dans un référentiel sphérique centré sur le point concourant, et
• à partir de la loi de commande déterminée lors de la calibration, en déduire une commande à appliquer au viseur pour viser l'objet.

The invention finally relates to the use of such a sighting system comprising the steps of:

• acquire a position of an object to be targeted in a repository of detection optics,
• deduce relative positions between the object and a point of intersection of the sighting lines of the viewfinder, coordinates of the object in a spherical frame centered on the concurrent point, and
• from the control law determined during the calibration, deduce a command to be applied to the viewfinder to aim the object.

The proposed calibration method has the advantage of being an automatic method and simple implementation by any sighting system.

This method does not require the development of a priori kinematic model of the system, which makes it possible to reduce the constraints of mechanical reproducibility of the system during manufacture and to reduce its cost. Constraints on system design to simplify the kinematic model are also relaxed.

In addition, the proposed method does not require shooting with an overlap area.

DESCRIPTION OF THE FIGURES

• La figure 1a représente un vue en deux dimensions schématique un système de visée,
• La figure 1b représente une vue en deux dimensions schématique d'un mode de réalisation alternatif du système de visée de la figure 1a.
• La figure 1c représente un exemple de référentiel pour la mesure des positions relatives d'un point à viser et d'un point concourant des lignes de visée du viseur du système de visée.
• Les figures 2a et 2b représentent schématiquement les principales étapes d'un procédé de calibration du système de visée selon deux modes de réalisation.
• La figure 3 représente schématiquement les étapes d'utilisation d'un système de visée calibrée selon le procédé de la figure 2a ou 2b.

Other features, objects and advantages of the present invention will appear on reading the detailed description which follows, with reference to the appended figures, given by way of non-limiting examples and in which:

• The figure 1a represents a schematic two-dimensional view of a sighting system,
• The figure 1b represents a schematic two-dimensional view of an alternative embodiment of the aiming system of the figure 1a .
• The figure 1c is an example of a repository for measuring the relative positions of a point to be aimed and a point in sight lines of sight of the aiming system.
• The Figures 2a and 2b schematically represent the main steps of a calibration method of the sighting system according to two embodiments.
• The figure 3 schematically represents the steps of using an aiming system calibrated according to the method of figure 2a or 2b .

DETAILED DESCRIPTION OF AT LEAST ONE EMBODIMENT OF THE INVENTION Aiming system

We have shown in figure 1a an example of a sighting system 1 that can be calibrated according to the method described below.

This sighting system 1 comprises at least one viewfinder 10, which can be an image acquisition device such as a camera. The viewfinder 10 is rotatable along two axes which are the yaw and the pitch, the rotation of the viewfinder along these two axes being actuated by a motor not shown.

The viewfinder 10 also has variable focus for focusing over a range of depths.

The aiming system 1 also comprises an optical 11 for detecting a position of an object O in space, for example in the form of two cameras. The position of the object O is located in the repository of the detection optics 11, which is a reference different from that of the viewfinder 10. This reference frame is fixed arbitrarily, and can if necessary be orthonormed.

We denote (x _i , y _i , z _i ) the coordinates of the object O in the repository of the detection optics.

We have shown on Figures 1a and 1b a non-limiting example of a reference system. In this case, this reference frame is orthogonal, has an axis z corresponding to a longitudinal axis of sight of the detection optics 11 and an axis x corresponding to the horizontal of the image obtained by this detection optics. This repository is the one that is used in the following.

Finally, the aiming system comprises a processing unit 12, for example an integrated circuit, comprising processing means adapted to control the rotation and the focusing of the viewfinder 10 by a control law from the position of the object. detected by the detection optics 11.

On the figure 1b , an alternative embodiment of the sighting system is shown, comprising a mirror 13 mounted between the object O to be aimed and the sighting system, the mirror being rotatable along two axes. The viewfinder 10 is in this case fixed and is aimed at the mirror 13, and the rotation of the mirror makes it possible to move the sight line of the viewfinder 10 to aim at the object O.

In the following, it is assumed that in both cases there is a concurrency point M of all the lines of sight of the viewfinder 10. This point M corresponds to the intersection between the mirror 13 and the line of sight of the viewfinder 10 extending between the viewfinder and the mirror 13 in the case of the figure 1b .

On the figure 1a , considering that the viewfinder 10 is mounted according to a perfect patella whose center of rotation is on the optical axis, the point M corresponds to the center of rotation.

In the following, we exploit the relative positions of the object O and the point M, to deduce the control law of the viewfinder 10.

In particular, since the positions of the object O and the point M are recorded in the repository of the detection optics 11, the coordinates of the object O in this reference frame can be converted into spherical coordinates with respect to the point M. represented on the figure 1c the conversion of the coordinates of the point O in the spherical repository centered on the point M.

The spherical coordinates of the object O comprise two values of angles α and β and a distance value.

$${\beta }_i={\cos }^{-1}\left(\frac{y_i-y_M}{\Vert O-M\Vert }\right)$$

Où ∥O - M∥ est la distance entre le point O et le point M, notée ρ dans la suite.According to the foregoing example in which the repository of the detection optics 11 is an orthonormal repository, by noting x _M , y _M and z _M the coordinates of the concurrent point M in the repository of the detection optics 11, the coordinates α _i and β _i of the object O are written as follows: $${\alpha }_i={\tan }^{-1}\left(\frac{x_i-x_M}{z_i-z_M}\right)$$

$${\beta }_i={\cos }^{-1}\left(\frac{{\mathrm{there}}_i-{\mathrm{there}}_M}{\Vert O-M\Vert }\right)$$

Where ∥ O - M ∥ is the distance between the point O and the point M, noted ρ in the following.

Calibration process

The calibration process, whose main steps are represented on the Figures 2a and 2b , includes the determination of a control law {C _y , C _p , C _d } to be applied to the viewfinder to aim at an object O, and the determination of the position of the point along the lines of sighting M.

This method is implemented by the aiming system 1, in particular step 200 is implemented by the processing means of the processing unit, by executing an appropriate program.

The control law comprises two angular commands C _y , C _p , these commands being commands of rotation of the viewfinder respectively yaw and pitch to be applied to the viewfinder to be oriented towards the object O.

The two angular commands are determined as a function of the position of the object O to be aimed with respect to the point M. They are therefore a function of the angles α and β: C _y (α, β), C _p (α, β), α and β depending themselves on the position of the point M.

The control law also comprises a focusing control C _d (ρ) of the viewfinder as a function of the distance ρ between the concurrent point of the lines of sight M and the object O, ρ depending itself on the position of the point Mr.

We note the control law C = {C _y (α, β), C _p (α, β), C _d (ρ)}

The method comprises a first acquisition step 100 of n target object reference positions and corresponding commands to be applied to the viewfinder to aim at the positions, where n is an integer greater than or equal to 6. P _{i denotes} the reference positions acquired during this step, C _yi , C _pi the corresponding angular commands and C _di corresponding _debug commands.

This step 100 is advantageously implemented by means of a test pattern equipped with several bar codes, and positioned in at least two different positions.

The viewfinder 10 can be manually controlled to be positioned so as to successively acquire a sharp image of each of the barcodes of the target (this corresponds to both a target accuracy and focus accuracy).

Alternatively, the viewfinder can acquire images of the target without being controlled to specifically target a barcode, and the target position is determined a posteriori according to what appears on the image, preferably by reading a barcode appearing on the image.

Advantageously, the test pattern comprises at least ten or even twenty barcodes, which correspond to as many positions P _i , and the target is itself positioned in several places with respect to the viewfinder to multiply the number of positions P _i .

Each position P _i is acquired in the repository of the detection optics 11.

Once a barcode of the target correctly aimed, it raises the angular commands C _yi , C _pi and focus C _di corresponding to the viewfinder 10.

Then the method comprises a step 200 of determining the position of the concurrent point M and the commands C _y , C _p , C _d constituting the control law.

This step is implemented by determining the minimum of a function of the second derivative of the control law. In this way the commands obtained are the least chaotic for a position of the object O fixed, so the most robust in case of inaccuracy on the measurement of the position of the object O.

The function to be minimized, which can be called the deformation energy of the control law, is the integral of the sum of the second derivatives of the commands composing the control law.

Où k est une constante prédéterminée de pondération, par exemple égale à 1.It is written as follows: $$\begin{array}{l}f={\displaystyle \iint {\Vert \frac{d^2{\mathrm{VS}}_{\mathrm{there}}}{d{\alpha }^2}\Vert }^2}+2{\Vert \frac{d^2{\mathrm{VS}}_{\mathrm{there}}}{\mathit{d\alpha d\beta }}\Vert }^2+{\Vert \frac{d^2{\mathrm{VS}}_{\mathrm{there}}}{d{\beta }^2}\Vert }^2\mathit{d\alpha d\beta }\\ +{\displaystyle \iint {\Vert \frac{d^2{\mathrm{VS}}_p}{d{\alpha }^2}\Vert }^2+2{\Vert \frac{d^2{\mathrm{VS}}_p}{\mathit{d\alpha d\beta }}\Vert }^2+{\Vert \frac{d^2{\mathrm{VS}}_p}{\mathit{d\beta }}\Vert }^2\mathit{d\alpha d\beta }+k}{\displaystyle \int {\Vert \frac{d^2{\mathrm{VS}}_d}{d{\rho }^2}\Vert }^2}\mathit{d\rho }\end{array}$$

Where k is a predetermined weighting constant, for example equal to 1.

According to a first embodiment represented in figure 2a this step is carried out by first determining, during a sub-step 210, the angular commands C _y , C _p , then in a second step the focus control C _d .

This step 210 is implemented by iteratively determining 211 the optimal position of the point M corresponding to the commands C _y , C _p minimizing the function f, then determining 212 the angular commands minimizing said function after the point M determined at the first time. the result of step 211.

The step 211 for determining the optimal position of the point M can be implemented in different ways.

According to a first possibility, f * denotes the term f corresponding only to the angular commands (f deprived of its term as a function of the focus control C _d ). $$f^{*}={\displaystyle \iint {\Vert \frac{d^2{\mathrm{VS}}_{\mathrm{there}}}{d{\alpha }^2}\Vert }^2}+2{\Vert \frac{d^2{\mathrm{VS}}_{\mathrm{there}}}{\mathit{d\alpha d\beta }}\Vert }^2+{\Vert \frac{d^2{\mathrm{VS}}_{\mathrm{there}}}{d{\beta }^2}\Vert }^2\mathit{d\alpha d\beta }+{\displaystyle \iint {\Vert \frac{d^2{\mathrm{VS}}_p}{d{\alpha }^2}\Vert }^2}+2{\Vert \frac{d^2{\mathrm{VS}}_p}{\mathit{d\alpha d\beta }}\Vert }^2+\Vert \frac{d^2{\mathrm{VS}}_p}{d{\beta }^2}\Vert \mathit{d\alpha d\beta }$$

Since it is known to determine argmin _{C y , C p} ( f * ( M, C _y , C _p )) to M fixed (the obtaining of minimizing commands f * is described hereinafter in step 212, which describes this step for the particular case of the optimal M), that is to say that it is known to calculate the functions C _y and C _p minimizing the function f *.

We denote F * the function of R ³ in R defined as follows: $$F^{*}\left(M\right)=\mathit{mid}{\mathrm{not}}_{{\mathrm{VS}}_{\mathrm{there}},{\mathrm{VS}}_p}\left(f^{*}\left(M,\mathrm{}{\mathrm{VS}}_{\mathrm{there}},\mathrm{}{\mathrm{VS}}_p\right)\right)$$

The step 211 for determining the optimal position of the point M is a step of minimizing the function F * (resp, G *). This step can be implemented by gradient descent.

• Détermination d'une position du point M,
• Calcul de C_y, C_p minimisant f* à M fixé,
• Ajustement itératif de la valeur du point M pour déterminer de nouveaux C_y, C_p minimisant f*.

It is implemented iteratively as follows:

• Determination of a position of the point M,
• Calculation of C _y , C _p minimizing f * to M fixed,
• Iterative adjustment of the value of the point M to determine new C _y , C _p minimizing f *.

According to a second possibility, it is possible to invert the calculation by expressing the angles α and β according to the commands C _y , C _p and not the opposite. We obtain the function g * such that: $$\begin{array}{l}{\mathrm{boy\; Wut}}^{*}={\displaystyle \iint {\Vert \frac{d^2\alpha }{d{\mathrm{VS}}_{\mathrm{there}}{}^2}\Vert }^2}+2{\Vert \frac{d^2\alpha }{d{\mathrm{VS}}_{\mathrm{there}}d{\mathrm{VS}}_p}\Vert }^2+{\Vert \frac{d^2\alpha }{d{\mathrm{VS}}_p{}^2}\Vert }^{2}d{\mathrm{VS}}_{\mathrm{there}}d{\mathrm{VS}}_p\\ +{\displaystyle \iint {\Vert \frac{d^2\beta }{d{\mathrm{VS}}_{\mathrm{there}}{}^2}\Vert }^2+2{\Vert \frac{d^2\beta }{d{\mathrm{VS}}_{\mathrm{there}}d{\mathrm{VS}}_p}\Vert }^2+{\Vert \frac{d^2\beta }{d{\mathrm{VS}}_p{}^2}\Vert }^{2}d{\mathrm{VS}}_{\mathrm{there}}d{\mathrm{VS}}_p}\end{array}$$

In this case, step 211 comprises determining the position of the point M minimizing the function G *, defined from R ³ in R as follows: $${\mathrm{BOY\; WUT}}^{*}\left(M\right)=\mathit{mid}{\mathrm{not}}_{\alpha ,\beta }\left({\mathrm{boy\; Wut}}^{*}\left(M,\alpha ,\beta \right)\right)$$

This step is implemented iteratively by calculating, for example by gradient descent, by calculating, for each position of the point M, the angles α and β expressed as a function of the commands C _y , C _p minimizing the function g *, then adjusting the position of the point M.

At the end of step 211, whatever the variant implemented, an optimum position of the point M is thus obtained.

It is then possible to determine during a step 212 the angular commands C _y , C _p minimizing f * for this position of the point M.

$$C_p\left(\alpha \left(P_i-M\right),\beta \left(P_i-M\right)\right)=C_{p_i}$$

pour i=1,..,n où n est le nombre de positions de référence relevées lors de l'étape 100.The minimization of this term is carried out taking into account the constraints that result from step 100, according to which: $${\mathrm{VS}}_{\mathrm{there}}\left(\alpha \left(P_i-M\right),\beta \left(P_i-M\right)\right)={\mathrm{VS}}_{{\mathrm{there}}_i}$$

$${\mathrm{VS}}_p\left(\alpha \left(P_i-M\right),\beta \left(P_i-M\right)\right)={\mathrm{VS}}_{p_i}$$

for i = 1, .., n where n is the number of reference positions found in step 100.

According to the article FL Bookstein, Main Warps: Thin-Plate Splines and the Decomposition of Deformations, IEEE Transactions on Pattern Analysis and Machine Intelligence Vol. 11, No 6, of June 1989 , the angular commands minimizing the function f * to M fixed are the type of thin-plate spline (in English TPS or Thin-Plate Spline).

Avec : $$U\left(r\right)=r^2\log \left(r^2\right)$$

Les points P_i correspondent aux n points obtenus à l'étape 100, et auxquels correspondent des valeurs d'angles α_i, β_i respectives. Le fait d'avoir au moins 6 points P_i permet d'obtenir au moins autant de points connus que de degrés de libertés (3 degrés de liberté pour a ₁, a_α et a_β et trois autres pour la position du point M).The angular command C _y (resp.c. C _p ) can be written as follows: $${\mathrm{VS}}_{\mathrm{there}}\left(\alpha ,\beta \right)={\mathrm{at}}_1+{\mathrm{at}}_{\alpha }\alpha +{\mathrm{at}}_{\beta }\beta +{\displaystyle \underset{i=1}{\overset{\mathrm{not}}{\Sigma }}{w}_{i}U\left(\left|\left(\alpha \left(P_i-M\right),\beta \left(P_i-M\right)\right)-\left(\alpha ,\beta \right)\right|\right)}$$

With: $$U\left(r\right)=r^2\log \left(r^2\right)$$

The points P _i correspond to the n points obtained in step 100, and to which correspond values of respective angles α _i , β _i . The fact of having at least 6 points P _i makes it possible to obtain at least as many known points as degrees of freedom (3 degrees of freedom for a ₁ , a _α and a _β and three others for the position of the point M) .

× n
où |P_i-P_j| est la distance entre les points P_i et P_j, $$Q=\left[\begin{array}{lll}1& {\alpha }_1& {\beta }_1\\ 1& {\alpha }_2& {\beta }_2\\ \dots & \dots & \dots \\ 1& {\alpha }_n& {\beta }_n\end{array}\right],n\times 3$$

et $$L=\left[\begin{array}{cc}K& Q\\ Q^T& 0\end{array}\right],\left(n+3\right)\times \left(n+3\right)$$

Où Q^T est la transposée de Q et O est une matrice nulle 3x3.We define the matrices: $$K=\left[\begin{array}{cccc}0& U\left(\left|\left({\alpha }_1,{\beta }_1\right)-\left({\alpha }_2,{\beta }_2\right)\right|\right)& ...& U\left(\left|\left({\alpha }_1,{\beta }_1\right)-\left({\alpha }_{\mathrm{not}},{\beta }_{\mathrm{not}}\right)\right|\right)\\ U\left(\left|\left({\alpha }_2,{\beta }_2\right)-\left({\alpha }_1,{\beta }_1\right)\right|\right)& 0& ...& U\left(\left|\left({\alpha }_2,{\beta }_2\right)-\left({\alpha }_1,{\beta }_1\right)\right|\right)\\ ...& ...& ...& ...\\ U\left(\left|\left({\alpha }_{\mathrm{not}},{\alpha }_{\mathrm{not}}\right)-\left({\alpha }_1,{\beta }_1\right)\right|\right)& U\left(\left|\left({\alpha }_{\mathrm{not}},{\beta }_{\mathrm{not}}\right)-\left({\alpha }_2,{\beta }_2\right)\right|\right)& ...& 0\end{array}\right],\mathrm{not}$$

× n
where | P _i -P _j | is the distance between the points P _i and P _j , $$Q=\left[\begin{array}{lll}1& {\alpha }_1& {\beta }_1\\ 1& {\alpha }_2& {\beta }_2\\ ...& ...& ...\\ 1& {\alpha }_{\mathrm{not}}& {\beta }_{\mathrm{not}}\end{array}\right],\mathrm{not}\times 3$$

and $$\mathrm{The}=\left[\begin{array}{cc}K& Q\\ Q^T& 0\end{array}\right],\left(\mathrm{not}+3\right)\times \left(\mathrm{not}+3\right)$$

Where Q ^T is the transpose of Q and O is a 3x3 null matrix.

Let V = ( v ₁ , ..., v _n ) be a vector of length n corresponding to the commands C _yi (resp.c C _pi ) acquired during step 100, and Y = ( V | 0 0 0) a column vector of dimension n. The vector W = ( w ₁ , ..., w _n ) and the coefficients a ₁ , a _α , and a _β are provided by the equation: $${\mathrm{The}}^{-1}Y={\left(W|\begin{array}{ccc}{\mathrm{at}}_1& {\mathrm{at}}_{\alpha }& {\mathrm{at}}_{\beta }\end{array}\right)}^T.$$

Advantageously, but optionally, the angular commands C _y , C _p may be regularized thin plate spline functions, as described in the publication of G. Donato and S. Belongie, Approximate Thin Plate Spline Mappings, Computer Vision - ECCV 2002, Springer Berlin Heldelberg, 2002, 21-31 .

The use of regularized splines makes it possible to release the constraint on the angular commands at the reference points P _i referred to during step 100 (the commands obtained do not take exactly the values C _yi and C _pi if the object is find in the position P _i ) and thus to take into account the possible noise measurement. This makes it possible to obtain a more robust control law.

où λ est une constante pré-déterminée, par exemple égale à 1In practice, according to an advantageous embodiment, during step 100, the commands C _y and C _p are not the commands minimizing exactly the function f *, but approaching the minimum. The minimized function is therefore not f * but a function f _r defined as the sum of f * and residual errors: $$f_r=f^{*}+\lambda {\displaystyle \Sigma {\left({\mathrm{VS}}_{\mathrm{there}}\left(\alpha \left(P_i-M\right),\beta \left(P_i-M\right)\right)-{\mathrm{VS}}_{{\mathrm{there}}_i}\right)}^2+{\left({\mathrm{VS}}_p\left(\alpha \left(P_i-M\right),\beta \left(P_i-M\right)\right)-{\mathrm{VS}}_{p_i}\right)}^2}$$

where λ is a pre-determined constant, for example equal to 1

The expressions of C _y and C _p obtained during the minimization of the function f _r are identical to those obtained for the minimization of f *, but with different values for the a ₁ , a _α and a _β and the w _i .

Back to the figure 2a the method also includes a step 220 of determining the focus control C _d .

avec U _1D (r) = r ³, et la contrainte qui résulte de l'étape 100, selon laquelle : $$C_d\left(\rho \left(P_i-M\right)\right)=C_{d_i}$$

This step includes minimizing the function f including the term related to the focus control, denoted f _d (f = f * + f _d ) having M, C _y and C _p set. As a variant, only the term f _d related to the debugging command is minimized, this variant being equivalent because f * does not depend on the control C _d of debugging. D. Eberly's paper, Thin-Plate Splines, Geometric Tools LLC, at www.geometrictools.com teaches the solution to minimizing function f _d . The focus control C _d obtained is a cubic spline, which is written as follows: $$\mathit{CD}={\mathrm{at}}_1+{\mathrm{at}}_{\rho }\rho +{\displaystyle \underset{i=1}{\overset{\mathrm{not}}{\Sigma }}{w}_i{U}_{1D}\left(\left|\rho -\rho \left(P_i-M\right)\right|\right)}$$

with U _{1 D} ( r ) = r ³ , and the constraint resulting from step 100, wherein: $${\mathrm{VS}}_d\left(\rho \left(P_i-M\right)\right)={\mathrm{VS}}_{d_i}$$

The calculations of the coefficients a ₁ , a _ρ and w _i are analogous to the above description concerning the calculation of regularized thin plate splines: definition of matrices K, Q and L and obtaining coefficients from the matrix L and a vector V comprising the focusing commands Cd _i corresponding to the known positions P _i .

According to an alternative embodiment represented in figure 2b during step 200, the angular and debugging commands are calculated simultaneously.

In this case, the command determining step is noted 200, this step also being an iterative step comprising the implementation, successively, of a first substep 211 'in which the optimum position of the point M is determined. , by determining the commands C _y , C _p , C _d minimizing the function f at each fixed M, and a second substep 212 'during which the commands C _y , C _p and C _d are determined at the point Fixed optimal M resulting from step 211 '.

• La position d'un objet O dans le référentiel de l'optique de détection 11 est déterminée au cours d'une étape 410.
• A partir de la position de l'objet O et de la position du point M, déterminée lors du procédé de calibration, on en déduit 420 les valeurs des angles α et β et de la distance d entre l'objet O et le point M.
• Puis, la loi de commande déterminée lors du procédé de calibration permet d'en déduire 430 les commandes à appliquer au moteur et au viseur pour viser précisément l'objet O.

Once the control law has been determined, the aiming system is used as follows, and as illustrated in figure 3 :

• The position of an object O in the repository of the detection optics 11 is determined during a step 410.
• From the position of the object O and the position of the point M, determined during the calibration process, 420 is deduced from the values of the angles α and β and from the distance d between the object O and the point M .
• Then, the control law determined during the calibration process makes it possible to deduce from it 430 the commands to be applied to the motor and the viewfinder in order to aim precisely at the object O.

The proposed method has the advantage of being able to be implemented on any sighting system without prior knowledge of its kinematic model. It does not induce constraints on the design or use of the system.

The method has a preferred application for the acquisition of remote iris images. In this case, the aiming system 1 comprises, as the viewfinder 10, a narrow-field, high-resolution mobile camera, for example a resolution of the order of 200 dpi to one meter.

The detection optics 11 comprises two fixed cameras with a relatively lower resolution than the viewfinder, for example of the order of 30 dpi at one meter, and a field relatively wider than the viewfinder, in order to be able to locate in a scene a iris of an individual whose image one wishes to acquire.

The position of the iris is acquired by the detection optics and communicated to the viewfinder which, having been calibrated by the method described above, can be positioned to accurately aim the iris and acquire an image.

This method also makes it possible to target an object such as an iris in a scene even if its position is not known a priori. This is therefore less restrictive for users whose iris image is acquired because they do not have to position themselves in a particular way or at a specific place so that an image of their iris can be acquired.

The method is nevertheless not limited to the field of acquisition of biometric feature images but is applicable to any object that is desired to be aimed by a sighting system.

Claims (11)

1. A method for calibrating a system for acquiring images of biometric features of individuals, said system comprising a viewfinder (10) and an optics (11) for detecting the position of an object (O) in space, characterized in that said calibration method comprises the determination of a control law to be applied to the viewfinder (10) to sight the object (O) depending on its position, said position being determined in a reference frame of the detection optics (11) and the control law comprising two angular controls (C_y, C_p) and a focus control (Cd) of the viewfinder (10), expressed as a function of the relative positions between the object to be sighted (O) and a concurrent point (M) of all lines of sight of the viewfinder (10),
   the calibration method comprising the steps consisting of:

   - sighting (100), with the viewfinder (10), objects located at least at six different reference positions (P_i) known in the reference frame of the detection optics (11) and noting the corresponding controls (C_yi, C_pi, C_di) for each reference position,

   - from the reference positions (P_i) and the corresponding controls (C_yi, C_pi, C_di) for each reference position, determining (200, 200') the position of the concurrent point (M) of the lines of sight and the control law (C_y, C_p) by minimizing a function of the second derivative of the control law by taking into account, as constraints, the controls (C_yi, C_pi, C_di), noted for the various sighted points (P_i).
2. The method for calibrating a system for acquiring images of biometric features of individuals according to claim 1, wherein the step of determining (200, 200') the position of the concurrent point (M) and the control law comprises the implementation of the steps consisting of:

   - determining (211, 211') a position of the concurrent point (M) corresponding to controls (C_y, C_p, C_d) minimizing the function of the second derivative of the control law, and

   - once the position of the concurrent point (M) is determined, determining (212, 212') the controls (C_y, C_p, C_d) minimizing the function of the second derivative of the control law.
3. The calibration method according to claim 2, wherein the step of determining (211, 211') the position of the concurrent point (M) comprises the minimization, depending on said position, of the integral of the sum of the second derivatives of the angular controls (C_y, C_p).
4. The calibration method according to claim 2, wherein the step of determining (211, 211') the position of the concurrent point (M) comprises the minimization, depending on said position, of the integral of the sum of the second derivatives of the relative angular positions between the point to be sighted (O) and the concurrent point (M), expressed as a function of the angular controls of the viewfinder (α(C_y, C_p), β(C_y, C_p)).
5. The calibration method according to any of the preceding claims, wherein each angular control (C_y, C_p) is a function of two angles (α, β) of the thin-plate spline type.
6. The calibration method according to claim 5, wherein each angular control (C_y, C_p) is a function of two angles (α, β) of the regularized thin-plate spline type.
7. The calibration method according to any of claims 2 to 6, wherein the determination of the focus control is implemented when determining the angular controls (C_y, C_p) or subsequently to the determination of the angular controls and the point M.
8. The calibration method according to claim 7, wherein the determination of the focus control (220, 211') comprises the minimization of the integral of the second derivative of the focus control.
9. The calibration method according to any of the preceding claims, wherein the focus control (C_d) is a function of the cubic spline type.
10. A system (1) for acquiring images of biometric features of individuals, comprising a viewfinder (10), an optics (11) for detecting a position of an object to be sighted, and a processing unit (12) including processing means, the system (1) for acquiring images of biometric features of individuals being characterized in that it is adapted to implement the method according to any of the preceding claims.
11. A use of a system (1) for acquiring images of biometric features of individuals according to the preceding claim, comprising the steps consisting of:

    - acquiring (410) a position of an object (O) to be sighted in a reference frame of the detection optics,

    - deducing (420) relative positions between the object (O) and a concurrent point (M) of the lines of sight of the viewfinder (10), coordinates of the object (O) in a spherical reference frame centered on the concurrent point (M), and

    - from the control law determined during the calibration method according to any of claims 1 to 9, deducing (430) therefrom a control to be applied to the viewfinder (10) to sight the object.

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